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Find the least value of f(x) = ax + \(\frac{b}{x}\),where a > 0, b > 0 and x > 0.

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Best answer

Since x > 0, a > 0, b > 0. 

By AM ≥ GM property,

(ax + \(\frac{b}{x}\)) ≥\(\sqrt a\times \sqrt b\).

So minimum value of f(x) is which occurs when  ax = \(\frac{b}{x}\)

i.e. x = \(\frac{\sqrt b}{\sqrt a}\)

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